Question

line y = 2x+1 is transformed by a dialation with a scale factor of two and centered at (0,-4). what is the equation of the image line

Answer 1

Answer: y = 2x + 6

Step-by-step explanation:

Here the equation of line,

y = 2x + 1

y-intercept of the line is, (0, 1)

And, the slope of the line is 2.

Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),

Then transformed point are get by,

$(x,y)\rightarrow (k(x-a)+a, k(y-b)+b)$

Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),

$(0,-4)\rightarrow (2(0-0)+0, 2(1+4)-4)$

$(0,-4)\rightarrow (0, 6)$

Thus, the point of the new line is (0,6)

And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)

Thus, the equation of new line,

(y - 6) = 2 (x - 0)

y - 6 = 2x

y = 2x + 6